Consider two polynomials and perform the subtraction in the two different orders.
A
a
False. See solution.
B
b
False. See solution.
Practice makes perfect
a
By definition, a binomial is the sum of two monomials and its degree is the greatest degree of its monomials. If the binomial has a degree of zero, it means that both monomials are constant.
Binomial = Monomial + Monomial
⇕
Binomial = Constant + Constant
Since the sum of two constants is a constant, the binomial will be formed by just one monomial. In other words, it will not be a binomial, but a monomial.
Binomial = Constant *
In consequence, we conclude that a binomial cannot have a degree of zero, which implies that the given statement is false.
b
To verify whether the given statement is true or not, let's consider the following two polynomials.
As we can see, the results are different. In the first case, we got 2 and in the second case we got -2. In conclusion, the order in which polynomials are subtracted does matter. The given statement is false.
